Neutrosophic Graphs Research Articles

NCMPy: A Modelling Software for Neutrosophic Cognitive Maps based on Python Package


 Cognitive maps are a vital tool that can be used for knowledge representation and reasoning. Fuzzy Cognitive Maps (FCMs) are popular soft computing techniques used to model large and complex systems, and they can aid in explainable artificial intelligence (AI). FCMs, however, cannot model the indeterminacy that arises in a system due to various uncertainties. Neutrosophic Cognitive Maps (NCMs), upgraded FCMs that could model indeterminacy, were introduced to address this issue. NCMs are a generalization of FCMs, a field of cognitive science firmly based on neural networks. NCMs have been used to solve a wide range of problems. NCMs were introduced in 2002, and even after 20 years, NCMs do not have any supportive software, package, toolbox, or visualization software like FCMs. The main reason for the absence of dedicated software is due to the indeterminacy concept 'I' and how it has to be handled. This paper presents the dedicated Python package created for handling the functioning of NCMs. The modelling software presented in this paper aids in visualizing the NCMs as a signed digraph with indeterminacy that is a directed signed neutrosophic graph. This package implements a sample case study using NCMs.

Novel Concepts on Domination in Neutrosophic Incidence Graphs with Some Applications

In graph theory, the concept of domination is essential in a variety of domains. It has broad applications in diverse fields such as coding theory, computer network models, and school bus routing and facility location problems. If a fuzzy graph fails to obtain acceptable results, neutrosophic sets and neutrosophic graphs can be used to model uncertainty correlated with indeterminate and inconsistent information in arbitrary real-world scenario. In this study, we consider the concept of domination as it relates to single-valued neutrosophic incidence graphs (SVNIGs). Given the importance of domination and its utilization in numerous fields, we propose the application of dominating sets in SVNIG with valid edges. We present some relevant definitions such as those of valid edges, cardinality, and isolated vertices in SVNIG along with some examples. Furthermore, we also show a few significant sets connected to the dominating set in an SVNIG such as independent and irredundant sets. We also investigate a relationship between the concepts of dominating sets and domination numbers as well as irredundant and independence sets in SVNIGs. Finally, a real-life deployment of domination in SVNIGs is investigated in relation to COVID-19 vaccination locations as a practical application.

Determination of various factors to evaluate a successful curriculum design using interval-valued Pythagorean neutrosophic graphs

Determination of various factors to evaluate a successful curriculum design using interval-valued Pythagorean neutrosophic graphs

Social network analysis by Turiyam graphs

ObjectiveA single valued neutrosophic set represented the uncertainty of real life situations in terms of membership (t), indeterminacy (i) and non-membership (f) degree. However, this uncertainty cannot be limited to those three degrees; there is also an additional refusal degree. For this issue, the Turiyam set is an appropriate tool, which described the neutrosophic refusal degree of this situation as a liberal (l) degree in addition to those three degrees. The graphical representation of this situation is required for knowledge processing. For this purpose, the Turiyam graph was introduced as an extension of the single valued neutrosophic graph. This graph is helpful when the depictions of the vertices or their relationships or both, are considered in terms of membership (t), indeterminacy (i), non-membership (f) and liberal (l) degrees. The goal of this paper is to introduce the degree, order and size in the context of Turiyam graphs and examine a social network (SN) with the help of this graph.ResultsIn this regard, the degree, order and size in the context of Turiyam graphs are studied. The feasibility of this Turiyam graph is shown by employing its concept in a social network (SN). Finally, the advantage of the Turiyam graph over the existing graph theories is recognized by viewing its better framework.

SOME CONTRIBUTION TO COMPLEMENT OF STRONG NEUTROSOPHIC GRAPHS

The Fundamental operations on Complement of Strong Neutrosophic Graphs. We have applied the concept of strong Neutrosophic Graphs and also some graphs are connected, we explore some Particular Cases of strong Neutrosophic Graphs.

Application of neutrosophic optimal network using operations

Neutrosophic graphs deals with more complex, uncertain problems in real-life applications which provides more flexibility and compatibility than Intuitionistic fuzzy graphs. The aim of this paper is to enrich the efficiency of the network in accordance with productivity and quality. Here we develop two Neutrosophic graphs into a fully connected Neutrosophic network using the product of graphs. Such a type of network is formed from individuals with unique aspects in every field of work among them. This study proposes extending the other graph products and forming a single valued Neutrosophic graph to find the efficient productivity in the flow of information on a single source network of a single valued Neutrosophic network. An Optimal algorithm is proposed and illustrated with an application.

Detecting influential node in a network using neutrosophic graph and its application

Detecting influential node in a network using neutrosophic graph and its application

Properties of interval-valued quadripartitioned neutrosophic graphs with real-life application

The interval-valued quadripartitioned neutrosophic set is represented by the partition of the interval-valued neutrosophic set’s indeterminacy function into contradiction and ignorance parts. This article introduces the properties of interval quadripartitioned single valued neutrosophic graph. The properties like complementary, self-complementary, strong and complete interval-valued quadripartitioned neutrosophic graphs are investigated. The finest illustration of locating a climate conducive to apricot cultivation in Ladakh is provided by the notion that has been offered. The model gives us details on the location that should be chosen for apricot farming. Using the proposed concepts, we highlight potential applications of the usual apricot plant that thrives in extremely cold climates and is appropriate for higher production. The adopted approach makes a superior fit to consider the problems in application viewpoint.

Closed neutrosophic dominating set in neutrosophic graphs

Closed neutrosophic dominating set in neutrosophic graphs

Complex fermatean neutrosophic graph and application to decision making

A new growing area of neutrosophic set (NS) theory called complex neutrosophic sets (CNS) provides useful tools for dealing with uncertainty in complex valued physical variables that are observed in the actual world. A CNS take values for the truth, indeterminacy and falsity membership functions in the complex plane's unit circle. In this research, a novel concept of complex fermatean neutrosophic graph (CFNG) is established. We proposed the order, size, degree and total degree of a vertex of CFNG. Also, we presented the primary operations such as complement, union, join, ring-sum and cartesian product of CFNG. Moreover, the concept of regular graph under complex fermatean neutrosophic environment is discussed. Finally, an application of multi criteria decision making problem in educational system to evaluate lecturer’s research productivity using CFNG is discussed.

Weiner Topological Index for Neutrosophic Graph based on Strong Domination Set and Number

Different topological indices will always be valuable in a variety of disciplines, including chemistry, economics, electronics, business studies, social sciences and medicine. According to the dominating set and number, the Wiener index for neutrosophic graphs (NG) will be studied in considerable detail in this research.
 Additionally, the Average Wiener index for an NG has been defined, and several associated theorems have been introduced.

Valued-inverse Dombi neutrosophic graph and application

<abstract><p>Utilizing two ideas of neutrosophic subsets (NS) and triangular norms, we introduce a new type of graph as valued-inverse Dombi neutrosophic graphs. The valued-inverse Dombi neutrosophic graphs are a generalization of inverse neutrosophic graphs and are dual to Dombi neutrosophic graphs. We present the concepts of (complete) strong valued-inverse Dombi neutrosophic graphs and analyze the complement of (complete) strong valued-inverse Dombi neutrosophic graphs and self-valued complemented valued-inverse Dombi neutrosophic graphs. Since the valued-inverse Dombi neutrosophic graphs depend on real values, solving the non-equation and the concept of homomorphism play a prominent role in determining the complete, strong, complementarity and self-complementarity of valued-inverse Dombi neutrosophic graphs. We introduce the truth membership order, indeterminacy membership order, falsity membership order, truth membership size, indeterminacy membership size and indeterminacy membership size of any given valued-inverse Dombi neutrosophic graph, which play a major role in the application of valued inverse Dombi neutrosophic graphs in complex networks. An application of a valued-inverse Dombi neutrosophic graph is also described in this study.</p></abstract>

Special types of bipolar single valued neutrosophic graphs

Special types of bipolar single valued neutrosophic graphs

Interval Valued Pentapartitioned Neutrosophic Graphs with an Application to MCDM

The concept of interval valued pentapartitioned neutrosophic set is the extension of interval-valued neutrosophic set, quadripartitioned neutrosophic set, interval valued quadripartitioned neutrosophic set and pentapartitioned neutrosophic set. The powerful mathematical tool known as the interval valued pentapartitioned neutrosophic set divides indeterminacy into three separate components: unknown, contradiction, and ignorance. There are several applications for graph theory in everyday life, and it is a rapidly growing topic. The concept of an interval valued pentapartitioned neutrosophic set is used in graph theory. A decision-making method ( multicriteria, MCDM) is proposed by using the developed Interval valued Pentapartitioned Neutrosophic set with a numerical illustration. In this paper, as an extension of interval valued neutrosophic graph theory, we introduce the notions of Interval-Valued Pentapartitioned Neutrosophic Graph (IVPPN-graph) with degree, size, and order of an IVPPN-graph.

Interval- valued fermatean neutrosophic graphs

In this work, we define Interval-valued Fermatean neutrosophic graphs and present some operations on Interval-valued Fermatean neutrosophic graphs. Further, we introduce the concepts of Regular interval-valued Fermatean neutrosophic graphs, Strong interval-valued Fermatean neutrosophic graphs, Cartesian, Composition, Lexicographic product of interval-valued Fermatean neutrosophic graphs. Finally, we give the applications of Interval-valued Fermatean neutrosophic graphs.

Quadripartitioned Neutrosophic Graph Structures

Quadripartitioned Neutrosophic Graph Structures

Recognition of the Pattern for Vertices to Make Dimension by Resolving in some Classes of Neutrosophic Graphs

Recognition of the Pattern for Vertices to Make Dimension by Resolving in some Classes of Neutrosophic Graphs

Regularity of Every Element to Function in the Type of Domination in Neutrosophic Graphs

Regularity of Every Element to Function in the Type of Domination in Neutrosophic Graphs

Seeking Empty Subgraphs To Determine Different Measurements in Some Classes of Neutrosophic Graphs

Seeking Empty Subgraphs To Determine Different Measurements in Some Classes of Neutrosophic Graphs

Impacts of Isolated Vertices To Cover Other Vertices in Neutrosophic Graphs

Impacts of Isolated Vertices To Cover Other Vertices in Neutrosophic Graphs